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Theorem bd0 15316
Description: A formula equivalent to a bounded one is bounded. See also bd0r 15317. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0.min BOUNDED 𝜑
bd0.maj (𝜑𝜓)
Assertion
Ref Expression
bd0 BOUNDED 𝜓

Proof of Theorem bd0
StepHypRef Expression
1 bd0.min . 2 BOUNDED 𝜑
2 bd0.maj . . 3 (𝜑𝜓)
32ax-bd0 15305 . 2 (BOUNDED 𝜑BOUNDED 𝜓)
41, 3ax-mp 5 1 BOUNDED 𝜓
Colors of variables: wff set class
Syntax hints:  wb 105  BOUNDED wbd 15304
This theorem was proved from axioms:  ax-mp 5  ax-bd0 15305
This theorem is referenced by:  bd0r  15317  bdth  15323  bdnth  15326  bdnthALT  15327  bdph  15342  bdsbc  15350  bdsnss  15365  bdcint  15369  bdeqsuc  15373  bdcriota  15375  bj-axun2  15407
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